The standard form of the equation of a circle can be expressed as:
(x – h)² + (y – k)² = r²
In this formula, (h, k) represents the coordinates of the center of the circle, and r is the radius.
Given the center at (2, 5), we have h = 2 and k = 5. The radius is given as 12, so r = 12.
Now we can substitute these values into the equation:
(x – 2)² + (y – 5)² = 12²
Calculating 12 squared gives us 144, so the equation simplifies to:
(x – 2)² + (y – 5)² = 144
This is the final equation of the circle with center at (2, 5) and radius 12.